Análise de um método quasi-isotrópico para mitigação de efeito de orientação de malha em simulação de escoamento bifásico em reservatórios de petróleo

Abstract

Mathematical models of oil reservoirs have been used for decades. These models consist of system of Partial Differential Equations that describe the flow of fluids within a porous medium along with a set of initial and boundary conditions. The reliability of the predictions depends on how well the mathematical model represents the physics of the phenomenon. As simplifying hypotheses are made to enable the numerical solution to be obtained, errors are introduced. In this way, different results are obtained for the same problem, depending on the orientation of the grid, and this effect, called the Grid Orientation Effect, is the focus of this work. Its reduction or elimination brings more reliability to the results obtained. This work proposes a Quasi-Isotropic method, which reconstructs values of velocity and total mobility at the edge in a way that leads to the truncation error becoming less anisotropic, for a cartesian mesh, applying this formulation in the simulation of oil reservoirs and comparing results with conventional formulations. The proposed method is applied in square meshes for three problems: advection-linear diffusion; standard 1/4th of 5 wells with piston-like constitutive relation; 3-well problem with a constitutive brooks-corey relation. When analyzing the performance of the Quasi-Isotropic Method in both oil reservoir problems, an improvement is observed in both, for all simulated cases, demonstrating the success obtained in the construction of the formulation.